Given:
WBC count is 10,000 per cubic millimeter of blood;
Blood volume is 5 liters;
60% of WBC are neutrophils;
Their average lifespan is 12 hours.
Question:
How many neutrophils need to be produced every hour on average to keep the count a constant?
To determine the number of neutrophils that need to be produced every hour to keep the count constant, we need to calculate the rate of neutrophil production required to compensate for their average lifespan.
First, let's calculate the number of neutrophils in the body:
Neutrophils = WBC count * percentage of neutrophils
Neutrophils = 10,000 * 0.60
Neutrophils = 6,000 neutrophils per cubic millimeter of blood
Next, let's calculate the total number of neutrophils in the entire blood volume:
Total Neutrophils = Neutrophils * Blood volume
Total Neutrophils = 6,000 * 5,000 (since 1 liter = 1,000 cubic millimeters)
Total Neutrophils = 30,000,000 neutrophils
Now, we need to determine the number of neutrophils that need to be produced every hour to compensate for their average lifespan of 12 hours:
Neutrophils to be produced per hour = Total Neutrophils / Average lifespan
Neutrophils to be produced per hour = 30,000,000 / 12
Neutrophils to be produced per hour ≈ 2,500,000 neutrophils
Therefore, approximately 2,500,000 neutrophils need to be produced every hour, on average, to maintain a constant neutrophil count.